Question

Find the total volume of the following composite figure with

h=7.5

and

r=3.6

Use 3.14 for LaTeX: \piπ.

Round to the nearest hundredth.

Answer 1

Given:

The height of the given fig = 7.5 unit

The radius of the given fig = 3.6 unit

To find the volume of the given composite figure.

Formula

The volume of the given fig

$V = V_{1}+V_{2}$

where,

$V_{1}$ be the volume of the cone

$V_{2}$ be the volume of the semicircle

$V_{1}=\pi r^{2} h$, r be the radius and h be the height

$V_{2} = \frac{2}{3} \pi r^{3}$, r be the radius

Now,

Putting, r= 3.6, h = 7.5 and π = 3.14 we get,

$V_{1} =(3.14)(3.6^{2} )(7.5)$ cube in

or, $V_{1}= 305.208$ cube in

And,

$V_{2} =\frac{2}{3} (3.14)(3.6^{3})$ cube in

or, $V_{2} = 97.67$ cube in

So,

$V = 305.208+97.67$ cube in

or, $V = 402.878$ = 402.88 cube in

Hence,

The volume of the given figure is 402.88 cube in.